Problem: $\dfrac{ -10w - 7x }{ -5 } = \dfrac{ -9w + 4y }{ -2 }$ Solve for $w$.
Multiply both sides by the left denominator. $\dfrac{ -10w - 7x }{ -{5} } = \dfrac{ -9w + 4y }{ -2 }$ $-{5} \cdot \dfrac{ -10w - 7x }{ -{5} } = -{5} \cdot \dfrac{ -9w + 4y }{ -2 }$ $-10w - 7x = -{5} \cdot \dfrac { -9w + 4y }{ -2 }$ Multiply both sides by the right denominator. $-10w - 7x = -5 \cdot \dfrac{ -9w + 4y }{ -{2} }$ $-{2} \cdot \left( -10w - 7x \right) = -{2} \cdot -5 \cdot \dfrac{ -9w + 4y }{ -{2} }$ $-{2} \cdot \left( -10w - 7x \right) = -5 \cdot \left( -9w + 4y \right)$ Distribute both sides $-{2} \cdot \left( -10w - 7x \right) = -{5} \cdot \left( -9w + 4y \right)$ ${20}w + {14}x = {45}w - {20}y$ Combine $w$ terms on the left. ${20w} + 14x = {45w} - 20y$ $-{25w} + 14x = -20y$ Move the $x$ term to the right. $-25w + {14x} = -20y$ $-25w = -20y - {14x}$ Isolate $w$ by dividing both sides by its coefficient. $-{25}w = -20y - 14x$ $w = \dfrac{ -20y - 14x }{ -{25} }$ Swap signs so the denominator isn't negative. $w = \dfrac{ {20}y + {14}x }{ {25} }$